Following a spirited display against the North London side, Clayton still harbours hopes of top-flight survival despite the club's winless run of 15 league games.
"If you asked the other teams 'Are Middlesbrough one of the three worst teams in the league?', I don't suppose many would say we are," the 28-year-old told reporters.
"We've played against teams and we have been in most games and have been pipped by that extra bit of quality that we need to have.
"There are more points to play for and nobody in the bottom three is pulling up trees and running clear...you have to keep believing."
On Saturday, Middlesbrough visit 16th-placed Bournemouth, who have slipped into the relegation scrap having failed to register a victory in their last four league games.
Clayton said his side were targeting three points at the Vitality Stadium to put pressure on other relegation candidates.
"Bournemouth will be a bit twitchy because they haven't won that many recently," Clayton added. "We need to put the pressure on them and see how they deal with it.
"And let's see what Swansea and Hull do with a bit of pressure on them. Three points will do that."
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty)
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